Hindawi
Wireless Communications and Mobile Computing
Volume 2018, Article ID 9713450, 24 pages
https://doi.org/10.1155/2018/9713450
Review Article
A Tutorial on Nonorthogonal Multiple Access
for 5G and Beyond
Mahmoud Aldababsa,1 Mesut Toka,1,2 Selahattin Gökçeli
GüneG Karabulut Kurt,3 and OLuz Kucur 1
,3
1
Electronics Engineering Department, Gebze Technical University, Gebze, 41400 Kocaeli, Turkey
Electrical and Electronics Engineering Department, Ömer Halisdemir University, 51240 Niğde, Turkey
3
Department of Communications and Electronics Engineering, Istanbul Technical University, 34469 Istanbul, Turkey
2
Correspondence should be addressed to Oğuz Kucur; okucur@gtu.edu.tr
Received 23 November 2017; Accepted 5 February 2018; Published 28 June 2018
Academic Editor: Nathalie Mitton
Copyright © 2018 Mahmoud Aldababsa et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
Today’s wireless networks allocate radio resources to users based on the orthogonal multiple access (OMA) principle. However,
as the number of users increases, OMA based approaches may not meet the stringent emerging requirements including very high
spectral efficiency, very low latency, and massive device connectivity. Nonorthogonal multiple access (NOMA) principle emerges
as a solution to improve the spectral efficiency while allowing some degree of multiple access interference at receivers. In this
tutorial style paper, we target providing a unified model for NOMA, including uplink and downlink transmissions, along with the
extensions to multiple input multiple output and cooperative communication scenarios. Through numerical examples, we compare
the performances of OMA and NOMA networks. Implementation aspects and open issues are also detailed.
1. Introduction
Wireless mobile communication systems became an indispensable part of modern lives. However, the number and
the variety of devices increase significantly and the same
radio spectrum is required to be reused several times by
different applications and/or users. Additionally, the demand
for the Internet of Things (IoT) introduces the necessity to
connect every person and every object [1]. However, current
communication systems have strict limitations, restricting
any modifications and improvements on the systems to meet
these demands. Recently, researchers have been working on
developing suitable techniques that may be integrated in next
generation wireless communication systems in order to fundamentally fulfill the emerging requirements, including very
high spectral efficiency, very low latency, massive device connectivity, very high achievable data rate, ultrahigh reliability,
excellent user fairness, high throughput, supporting diverse
quality of services (QoS), energy efficiency, and a dramatic
reduction in the cost [2]. Some potential technologies have
been proposed by the academia and the industry in order to
satisfy the aforementioned tight requirements and to address
the challenges of future generations. For example, millimeter
wave (mmWave) technology was suggested to enlarge the
transmission bandwidth for very high speed communications
[3], massive multiple input multiple output (MIMO) concept
was presented to improve capacity and energy efficiency [4],
and ultradense networks were introduced to increase the
throughput and to reduce the energy consumption through
using a large number of small cells [5].
Besides the aforementioned techniques, a new radio
access technology is also developed by researchers to be used
in communication networks due to its capability in increasing
the system capacity. Recently, nonorthogonality based system
designs are developed to be used in communication networks
and have gained significant attention of researchers. Hence,
multiple access (MA) techniques can now be fundamentally categorized as orthogonal multiple access (OMA) and
nonorthogonal multiple access (NOMA). In OMA, each
user can exploit orthogonal communication resources within
2
either a specific time slot, frequency band, or code in order to
avoid multiple access interference. The previous generations
of networks have employed OMA schemes, such as frequency
division multiple access (FDMA) of first generation (1G),
time division multiple access (TDMA) of 2G, code division
multiple access (CDMA) of 3G, and orthogonal frequency
division multiple access (OFDMA) of 4G. In NOMA, multiple users can utilize nonorthogonal resources concurrently by
yielding a high spectral efficiency while allowing some degree
of multiple access interference at receivers [6, 7].
In general, NOMA schemes can be classified into two
types: power-domain multiplexing and code-domain multiplexing. In power-domain multiplexing, different users are
allocated different power coefficients according to their channel conditions in order to achieve a high system performance.
In particular, multiple users’ information signals are superimposed at the transmitter side. At the receiver side successive
interference cancellation (SIC) is applied for decoding the
signals one by one until the desired user’s signal is obtained
[8], providing a good trade-off between the throughput of
the system and the user fairness. In code-domain multiplexing, different users are allocated different codes and
multiplexed over the same time-frequency resources, such as
multiuser shared access (MUSA) [9], sparse code multiple
access (SCMA) [10], and low-density spreading (LDS) [11].
In addition to power-domain multiplexing and code-domain
multiplexing, there are other NOMA schemes such as pattern
division multiple access (PDMA) [12] and bit division multiplexing (BDM) [13]. Although code-domain multiplexing
has a potential to enhance spectral efficiency, it requires a
high transmission bandwidth and is not easily applicable
to the current systems. On the other hand, power-domain
multiplexing has a simple implementation as considerable
changes are not required on the existing networks. Also, it
does not require additional bandwidth in order to improve
spectral efficiency [14]. In this review/tutorial paper, we will
focus on the power-domain NOMA.
Although OMA techniques can achieve a good system
performance even with simple receivers because of no mutual
interference among users in an ideal setting, they still do
not have the ability to address the emerging challenges due
to the increasing demands in 5G networks and beyond. For
example, according to International Mobile Telecommunications (IMT) for 2020 and beyond [15], 5G technology should
support three main categories of scenarios, such as enhanced
mobile broadband (eMBB), massive machine type communication (mMTC), and ultrareliable and low-latency communication (URLLC). The main challenging requirements of
eMBB scenario are 100 Mbps user perceived data rate and
more than 3 times spectrum efficiency improvement over
the former LTE releases to provide services including high
definition video experience, virtual reality, and augmented
reality. Since a large number of IoT devices will have access
to the network, the main challenge of mMTC is to provide
connection density of 1 million devices per square kilometer.
In case of URLLC, the main requirements include 0.5 ms
end-to-end latency and reliability above 99.999% [16–18]. By
using NOMA scheme, for mMTC and URLLC applications,
the number of user connections can be increased by 5 and
Wireless Communications and Mobile Computing
9 times, respectively [18]. Also, according to [19], NOMA has
been shown to be more spectral-efficient by 30% for downlink
and 100% for uplink in eMBB when compared to OMA.
Therefore, NOMA has been recognized as a strong candidate
among all MA techniques since it has essential features to
overcome challenges in counterpart OMA and achieve the
requirements of next mobile communication systems [20–
22]. The superiority of NOMA over OMA can be remarked
as follows:
(i) Spectral efficiency and throughput: in OMA, such as
in OFDMA, a specific frequency resource is assigned
to each user even it experiences a good or bad
channel condition; thus the overall system suffers
from low spectral efficiency and throughput. In the
contrary, in NOMA the same frequency resource is
assigned to multiple mobile users, with good and
bad channel conditions, at the same time. Hence, the
resource assigned for the weak user is also used by
the strong user, and the interference can be mitigated
through SIC processes at users’ receivers. Therefore,
the probability of having improved spectral efficiency
and a high throughput will be considerably increased
as depicted in Figure 1.
(ii) User fairness, low latency, and massive connectivity:
in OMA, for example in OFDMA with scheduling,
the user with a good channel condition has a higher
priority to be served while the user with a bad channel
condition has to wait for access, which leads to a fairness problem and high latency. This approach can not
support massive connectivity. However, NOMA can
serve multiple users with different channel conditions
simultaneously; therefore, it can provide improved
user fairness, lower latency, and higher massive connectivity [20].
(iii) Compatibility: NOMA is also compatible with the
current and future communication systems since it
does not require significant modifications on the
existing architecture. For example, NOMA has been
included in third generation partnership project longterm evolution advanced (3GPP LTE Release 13) [23–
29]. More detailed, in the standards, a downlink
version of NOMA, multiuser superposition transmission (MUST), has been used [23]. MUST utilizes
the superposition coding concept for a multiuser
transmission in LTE-A systems. In 3GPP radio access
network (RAN), while using MUST, the deployment
scenarios, evaluation methodologies, and candidate
NOMA scheme have been investigated in [24–26],
respectively. Then, system level performance and link
level performance of NOMA have been evaluated in
[27, 28], respectively. Next, 3GPP LTE Release 14 has
been proposed [29], in which intracell interference
is eliminated and hence LTE can support downlink intracell multiuser superposition transmission.
Also, NOMA, known as layered division multiplexing
(LDM), is used in the future digital TV standard,
ATSC 3.0 [30]. Moreover, the standardization study
of NOMA schemes for 5G New Radio (NR) continues
Wireless Communications and Mobile Computing
Power
3
OMA (OFDMA based)
Power
NOMA
Frequency
Frequency
Figure 1: A pictorial comparison of OMA and NOMA.
within 3GPP LTE Release 15 [31]. Agreed objectives in
Release 15 can be summarized as follows: (1) transmitter side signal processing schemes for NOMA,
such as modulation and symbol level processing,
coded bit level processing, and symbol to resource
element mapping; (2) receivers for NOMA, such
as minimum mean-square error (MMSE) receiver,
SIC and/or parallel interference cancellation (PIC)
receiver, joint detection type receivers, and complexity of the receivers; (3) NOMA procedures, such as
uplink transmission detection, link adaptation MA,
synchronous and asynchronous operation, and adaptation between OMA and NOMA; (4) link and system
level performance evaluation or analysis for NOMA,
such as traffic model and deployment scenarios of
eMBB, mMTC and URLLC, coverage, latency, and
signaling overhead.
In other words, the insufficient performance of OMA makes it
inapplicable and unsuitable to provide the features needed to
be met by the future generations of wireless communication
systems. Consequently, researchers suggest NOMA as a
strong candidate as an MA technique for next generations
[32]. Although NOMA has many features that may support
next generations, it has some limitations that should be
addressed in order to exploit its full advantage set. Those
limitations can be pointed out as follows. In NOMA, since
each user requires to decode the signals of some users before
decoding its own signal, the receiver computational complexity will be increased when compared to OMA, leading
to a longer delay. Moreover, information of channel gains
of all users should be fed back to the base station (BS),
but this results in a significant channel state information
(CSI) feedback overhead. Furthermore, if any errors occur
during SIC processes at any user, then the error probability
of successive decoding will be increased. As a result, the
number of users should be reduced to avoid such error
propagation. Another reason for restricting the number of
users is that considerable channel gain differences among
users with different channel conditions are needed to have a
better network performance.
This paper, written in a tutorial name, focuses on NOMA
technique, along with its usage in MIMO and cooperative
scenarios. Practice implementation aspects are also detailed.
Besides, an overview about the standardizations of NOMA in
3GPP LTE and application in the 5G scenarios is provided. In
addition, unlike previous studies, this paper includes performance analyses of MIMO-NOMA and cooperative NOMA
scenarios to make the NOMA concept more understandable
by researchers. The remainder of this paper is organized as
follows. Basic concepts of NOMA, in both downlink and
uplink networks, are given in Section 2. In Sections 3 and
4, MIMO-NOMA and cooperative NOMA are described,
respectively. Practical implementation challenges of NOMA
are detailed in Section 5. The paper is concluded in Section 6.
2. Basic Concepts of NOMA
In this section, an overview of NOMA in downlink
and uplink networks is introduced through signal-tointerference-and-noise ratio (SINR) and sum rate analyses.
Then, high signal-to-noise ratio (SNR) analysis has been
conducted in order to compare the performances of OMA
and NOMA techniques.
2.1. Downlink NOMA Network. At the transmitter side of
downlink NOMA network, as shown in Figure 2, the BS
transmits the combined signal, which is a superposition of
the desired signals of multiple users with different allocated
power coefficients, to all mobile users. At the receiver of each
user, SIC process is assumed to be performed successively
until user’s signal is recovered. Power coefficients of users
are allocated according to their channel conditions, in an
inversely proportional manner. The user with a bad channel
condition is allocated higher transmission power than the one
which has a good channel condition. Thus, since the user
with the highest transmission power considers the signals
of other users as noise, it recovers its signal immediately
4
Wireless Communications and Mobile Computing
Power
U1 signal
detection
U1
U1
SIC for U1
signal
U2 signal
detection
SIC for U1 , U2 , . . . , Ul−1
Ul signal
signals
detection
U2
U2
Base station
(BS)
s
Ul
Ul
UL
UL
Resource
SIC for U1 , U2 , . . . , UL−1
UL signal
signals
detection
Figure 2: Downlink NOMA network.
without performing any SIC process. However, other users
need to perform SIC processes. In SIC, each user’s receiver
first detects the signals that are stronger than its own desired
signal. Next, those signals are subtracted from the received
signal and this process continues until the related user’s own
signal is determined. Finally, each user decodes its own signal
by treating other users with lower power coefficients as noise.
The transmitted signal at the BS can be written as follows:
𝐿
𝑠 = ∑√𝑎𝑖 𝑃𝑠 𝑥𝑖 ,
(1)
where 𝛾 = 𝑃𝑠 /𝜎2 denotes the SNR. In order to find the
desired information of the 𝑙th user, SIC processes will be
implemented for the signal of user 𝑗 ≤ 𝑙. Thus, the SINR of
𝑙th user can be given by
SINR𝑙 =
𝐿
𝑦𝑙 = ℎ𝑙 𝑠 + 𝑛𝑙 = ℎ𝑙 ∑√𝑎𝑖 𝑃𝑠 𝑥𝑖 + 𝑛𝑙 ,
(2)
2.1.1. SINR Analysis. By using (2), the instantaneous SINR of
the 𝑙th user to detect the 𝑗th user, 𝑗 ≤ 𝑙, with 𝑗 ≠ 𝐿 can be
written as follows:
󵄨 󵄨2
𝑎𝑗 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
,
SINR𝑗→𝑙 = 󵄨 󵄨2 𝐿
(3)
𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ∑𝑖=𝑗+1 𝑎𝑖 + 1
(4)
󵄨 󵄨2
SINR𝐿 = 𝑎𝐿 𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨󵄨 .
(5)
2.1.2. Sum Rate Analysis. After finding the SINR expressions
of downlink NOMA, the sum rate analysis can easily be done.
The downlink NOMA achievable data rate of 𝑙th user can be
expressed as
𝑅𝑙NOMA-d = log2 (1 + SINR𝑙 )
= log2 (1 +
𝑖=1
where 𝑛𝑙 is zero mean complex additive Gaussian noise with
a variance of 𝜎2 ; that is, 𝑛𝑙 ∼ CN(0, 𝜎2 ).
.
󵄨 󵄨2
𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ∑𝐿𝑖=𝑙+1 𝑎𝑖 + 1
Then, the SINR of the 𝐿th user is expressed as
𝑖=1
where 𝑥𝑖 is the information of user 𝑖 (𝑈𝑖 ) with unit energy.
𝑃𝑠 is the transmission power at the BS and 𝑎𝑖 is the power
coefficient allocated for user 𝑖 subjected to ∑𝐿𝑖=1 𝑎𝑖 = 1 and
𝑎1 ≥ 𝑎2 ≥ ⋅ ⋅ ⋅ ≥ 𝑎𝐿 since without loss of generality the
channel gains are assumed to be ordered as |ℎ1 |2 ≤ |ℎ2 |2 ≤
⋅ ⋅ ⋅ ≤ |ℎ𝐿 |2 , where ℎ𝑙 is the channel coefficient of 𝑙th user,
based on NOMA concept. The received signal at 𝑙th user can
be expressed as follows:
󵄨 󵄨2
𝑎𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
󵄨 󵄨2
𝑎𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
󵄨 󵄨2
𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ∑𝐿𝑖=𝑙+1 𝑎𝑖 + 1
).
(6)
Therefore, the sum rate of downlink NOMA can be written as
𝐿
NOMA-d
= ∑log2 (1 + SINR𝑙 )
𝑅sum
𝑙=1
𝐿−1
= ∑ log2 (1 +
𝑙=1
󵄨 󵄨2
𝑎𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
󵄨 󵄨2
𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ∑𝐿𝑖=𝑙+1 𝑎𝑖 + 1
󵄨 󵄨2
+ log2 (1 + 𝑎𝐿 𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨󵄨 )
)
Wireless Communications and Mobile Computing
5
U1
U2
SIC for U1 , U2 , . . . , UL
Base station
signals
(BS)
x1
x2
r
xl
Ul
UL
xL
Figure 3: Uplink NOMA network.
𝐿−1
= ∑ log2 (1 +
𝑙=1
∑𝐿𝑖=𝑙+1 𝑎𝑖
𝑎𝑙
2.2.1. SINR Analysis. The BS decodes the signals of users
orderly according to power coefficients of users, and then the
SINR for 𝑙th user 𝑙 ≠ 1 can be given by [33]
󵄨 󵄨2 )
+ 1/𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
󵄨 󵄨2
+ log2 (1 + 𝑎𝐿 𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨󵄨 ) .
(7)
In order to figure out whether NOMA techniques outperform OMA techniques, we conduct a high SNR analysis.
Thus, at high SNR, that is, 𝛾 → ∞, the sum rate of downlink
NOMA becomes
NOMA-d
𝑅sum
𝐿−1
≈ ∑ log2 (1 +
𝑙=1
𝑎𝑙
∑𝐿𝑖=𝑙+1 𝑎𝑖
󵄨 󵄨2
) + log2 (𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨󵄨 )
SINR𝑙 =
󵄨 󵄨2
𝑎𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
,
󵄨󵄨 󵄨󵄨2
𝛾 ∑𝑙−1
𝑖=1 𝑎𝑖 󵄨󵄨ℎ𝑖 󵄨󵄨 + 1
where 𝛾 = 𝑃/𝜎2 . Next, the SINR for the first user is expressed
as
󵄨 󵄨2
SINR1 = 𝑎1 𝛾 󵄨󵄨󵄨ℎ1 󵄨󵄨󵄨 .
(8)
󵄨 󵄨2
≈ log2 (𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨󵄨 ) .
(10)
(11)
2.2.2. Sum Rate Analysis. The sum rate of uplink NOMA can
be written as
𝐿
2.2. Uplink NOMA Network. In uplink NOMA network, as
depicted in Figure 3, each mobile user transmits its signal to
the BS. At the BS, SIC iterations are carried out in order to
detect the signals of mobile users. By assuming that downlink
and uplink channels are reciprocal and the BS transmits
power allocation coefficients to mobile users, the received
signal at the BS for synchronous uplink NOMA can be
expressed as
𝐿
𝑟 = ∑ℎ𝑖 √𝑎𝑖 𝑃𝑥𝑖 + 𝑛,
(9)
NOMA-u
= ∑log2 (1 + SINR𝑙 )
𝑅sum
𝑙=1
󵄨 󵄨2
= log2 (1 + 𝑎1 𝛾 󵄨󵄨󵄨ℎ1 󵄨󵄨󵄨 )
󵄨 󵄨2
𝑎𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
+ ∑log2 (1 +
)
󵄨󵄨 󵄨󵄨2
𝛾 ∑𝑙−1
𝑙=2
𝑖=1 𝑎𝑖 󵄨󵄨ℎ𝑖 󵄨󵄨 + 1
𝐿
(12)
𝐿
󵄨 󵄨2
= log2 (1 + 𝛾∑𝑎𝑙 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ) .
𝑙=1
𝑖=1
where ℎ𝑖 is the channel coefficient of the 𝑖th user, 𝑃 is the
maximum transmission power assumed to be common for
all users, and 𝑛 is zero mean complex additive Gaussian noise
with a variance of 𝜎2 ; that is, 𝑛 ∼ CN(0, 𝜎2 ).
When 𝛾 → ∞, the sum rate of uplink NOMA becomes
𝐿
󵄨 󵄨2
NOMA-u
𝑅sum
≈ log2 (𝛾∑ 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ) .
𝑙=1
(13)
6
Wireless Communications and Mobile Computing
2.3. Comparing NOMA and OMA. The achievable data rate
of the 𝑙th user of OMA for both uplink and downlink can be
expressed as [33]
𝑅𝑙OMA = 𝛼𝑙 log2 (1 +
󵄨 󵄨2
𝛽𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
),
𝛼𝑙
(14)
where 𝛽𝑙 and 𝛼𝑙 are the power coefficient and the parameter
related to the specific resource of 𝑈𝑙 , respectively. And then,
the sum rate of OMA is written as
𝐿
OMA
= ∑𝛼𝑙 log2 (1 +
𝑅sum
𝑙=1
󵄨 󵄨2
𝛽𝑙 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨
).
𝛼𝑙
(15)
For OMA, for example, FDMA, total bandwidth resource
and power are shared among the users equally; then using
𝛼𝑙 = 𝛽𝑙 = 1/𝐿 the sum rate can be written as
𝐿
1
󵄨 󵄨2
OMA
𝑅sum
= ∑ log2 (1 + 𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ) .
𝐿
𝑙=1
(16)
When 𝛾 → ∞, the sum rate of OMA becomes
𝐿
1
󵄨 󵄨2
OMA
𝑅sum
≈ ∑ log2 (𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ) .
𝐿
𝑙=1
(17)
Using |ℎ1 |2 ≤ |ℎ2 |2 ≤ ⋅ ⋅ ⋅ ≤ |ℎ𝐿 |2 ,
𝐿
𝐿
1
1
󵄨 󵄨2
󵄨 󵄨2
OMA
≈ ∑ log2 (𝛾 󵄨󵄨󵄨ℎ𝑙 󵄨󵄨󵄨 ) ≤ ∑ log2 (𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨󵄨 )
𝑅sum
𝐿
𝐿
𝑙=1
𝑙=1
(18)
󵄨󵄨2
󵄨
NOMA-d
.
= log2 (𝛾 󵄨󵄨󵄨ℎ𝐿 󵄨󵄨 ) ≈ 𝑅sum
OMA
NOMA-d
≤ 𝑅sum
.
Hence, we conclude 𝑅sum
For the sake of simplicity, sum rates of uplink NOMA and
OMA can be compared for two users. Then, using (13) and
(17) the sum rate of uplink NOMA and OMA at high SNR
can be expressed, respectively, as
󵄨 󵄨2
󵄨 󵄨2
NOMA-u
𝑅sum
≈ log2 (𝛾 󵄨󵄨󵄨ℎ1 󵄨󵄨󵄨 + 𝛾 󵄨󵄨󵄨ℎ2 󵄨󵄨󵄨 ) ,
1
1
󵄨 󵄨2
󵄨 󵄨2
OMA
≈ log2 (𝛾 󵄨󵄨󵄨ℎ1 󵄨󵄨󵄨 ) + log2 (𝛾 󵄨󵄨󵄨ℎ2 󵄨󵄨󵄨 )
𝑅sum
2
2
󵄨 󵄨2
≤ log2 (𝛾 󵄨󵄨󵄨ℎ2 󵄨󵄨󵄨 ) .
(19)
(20)
OMA
NOMA-u
≤ 𝑅sum
.
From (19) and (20), we notice 𝑅sum
Figure 4 shows that NOMA outperforms OMA in terms
of sum rate in both downlink and uplink of two user networks
using (7), (12), and (16).
3. MIMO-NOMA
MIMO technologies have a significant capability of increasing capacity as well as improving error probability of wireless
communication systems [34]. To take advantage of MIMO
schemes, researchers have investigated the performance of
NOMA over MIMO networks [35]. Many works have been
studying the superiority of MIMO-NOMA over MIMOOMA in terms of sum rate and ergodic sum rate under
different conditions and several constrictions [36–39]. Specifically, in [36], the maximization problem of ergodic sum
rate for two-user MIMO-NOMA system over Rayleigh fading
channels is discussed. With the need of partial CSI at the
BS and under some limitations on both total transmission
power and the minimum rate for the user with bad channel
condition, the optimal power allocation algorithm with
a lower complexity to maximize the ergodic capacity is
proposed. However, in order to achieve a balance between
the maximum number of mobile users and the optimal
achievable sum rate in MIMO-NOMA systems, sum rate
has been represented through two ways. The first approach
targets the optimization of power partition among the user
clusters [37]. Another approach is to group the users in
different clusters such that each cluster can be allocated with
orthogonal spectrum resources according to the selected user
grouping algorithm [38]. Furthermore, in [37] performances
of two users per cluster schemes have been studied for
both MIMO-NOMA and MIMO-OMA over Rayleigh fading
channels. In addition, in accordance with specified power
split, the dominance of NOMA over OMA has been shown
in terms of sum channel and ergodic capacities.
On the other side, the authors in [38] have examined the
performance of MIMO-NOMA system, in which multiple
users are arranged into a cluster. An analytical comparison
has been provided between MIMO-NOMA and MIMOOMA, and then it is shown that NOMA outperforms OMA
in terms of sum channel and ergodic capacities in case of
multiple antennas. Moreover, since the number of users per
cluster is inversely proportional to the achievable sum rate
and the trade-off between the number of admitted users
and achieved sum rate has to be taken into account (which
restricts the system performance), a user admission scheme,
which maximizes the number of users per cluster based on
their SINR thresholds, is proposed. Although the optimum
performance is achieved in terms of the number of admitted
users and the sum rate when the SINR thresholds of all
users are equal, even when they are different good results
are obtained. In addition, a low complexity of the proposed
scheme is linearly proportional to the number of users per
cluster. In [39], the performance of downlink MIMO-NOMA
network for a simple case of two users, that is, one cluster,
is introduced. In this case, MIMO-NOMA provides a better
performance than MIMO-OMA in terms of both the sum
rate and ergodic sum rate. Also, it is shown that for a more
practical case of multiple users, with two users allocated into
a cluster and sharing the same transmit beamforming vector,
where ZF precoding and signal alignment are employed at the
BS and the users of the same cluster, respectively, the same
result still holds.
Antenna selection techniques have also been recognized
as a powerful solution that can be applied to MIMO systems
in order to avoid the adverse effects of using multiple
antennas simultaneously. These effects include hardware
complexity, redundant power consumption, and high cost.
Meanwhile diversity advantages that can be achieved from
MIMO systems are still maintained [40]. Several works apply
Wireless Communications and Mobile Computing
7
20
18
18
16
16
14
14
Sum rate (bps/Hz)
Sum rate (bps/Hz)
Downlink network
20
12
10
8
12
10
8
6
6
4
4
2
0
5
10 15 20 25 30 35 40 45 50
Signal to noise ratio (dB)
NOMA
OMA
Uplink network
2
0
5
10 15 20 25 30 35 40 45 50
Signal to noise ratio (dB)
NOMA
OMA
Figure 4: Sum rate of NOMA and OMA in both downlink and uplink networks with 𝑎1 = 0.6, 𝑎2 = 0.4, |ℎ1 |2 = 0 dB, and |ℎ2 |2 = 20 dB.
antenna selection techniques in MIMO-NOMA as they have
already been developed for MIMO-OMA systems. But the
gains can not be easily replicated since there is a heavy
interuser interference in MIMO-NOMA networks, dissimilar
from those in MIMO-OMA networks, in which information
is transmitted in an interference-free manner. Consequently,
there are a few works that challenged the antenna selection
problem [41–43]. In [41], the sum rate performance for downlink multiple input single output- (MISO-) NOMA system is
investigated with the help of transmit antenna selection (TAS)
at the BS, where the transmitter of the BS and the receiver
of each mobile user are equipped with multiantenna and
single antenna, respectively. Basically, in TAS-OMA scheme,
the best antenna at the BS offering the highest SINR is
selected. However in the proposed TAS-NOMA scheme in
[41], the best antenna at the BS providing the maximum
sum rate is chosen. In addition to using an efficient TAS
scheme, user scheduling algorithm is applied in two user
massive MIMO-NOMA system in order to maximize the
achievable sum rate in [42] for two scenarios, namely, the
single-band two users and the multiband multiuser. In the
first scenario, an efficient search algorithm is suggested. This
algorithm aims to choose the antennas providing the highest
channel gains in such a way that the desired antennas are only
searched from specified finite candidate set, which are useful
to the concerned users. On the other hand, in the second
scenario, a joint user and antenna contribution algorithm
is proposed. In particular, this algorithm manipulates the
ratio of channel gain specified by a certain antenna-user
pair to the total channel gain, and hence antenna-user pair
offering the highest contribution to the total channel gain is
selected. Moreover, an efficient search algorithm provides a
better trade-off between system performance and complexity,
rather than a joint antenna and user contribution algorithm.
Unfortunately, neither the authors of [41] nor the authors
of [42] have studied the system performance analytically.
In [43], the maximization of the average sum rate of twouser NOMA system, in which the BS and mobile users are
equipped with multiantenna, is discussed through two computationally effective joint antenna selection algorithms; the
max-min-max and the max-max-max algorithms. However,
the instantaneous channel gain of the user with a bad channel
condition is improved in max-min-max antenna selection
scheme while max-max-max algorithm is the solution for the
user with a good channel condition. Furthermore, asymptotic
closed-form expressions of the average sum rates are evaluated for both proposed algorithms. Moreover, it is verified
that better user fairness can be achieved by the max-min-max
algorithm while larger sum rate can be obtained by the maxmax-max algorithm.
Multicast beamforming can also be introduced as a technique that can be employed in MIMO schemes since it offers
a better sum capacity performance even for multiple users.
However, it can be applied in different ways. One approach
is based on a single beam that can be used by all users;
hence all users receive this common signal [44]. Another
approach is to use multiple beams that can be utilized by
many groups of users; that is, each group receives a different
signal [45]. The following works have studied beamforming
in MIMO-NOMA systems. In [46], multiuser beamforming
in downlink MIMO-NOMA system is proposed. Particularly,
a pair of users can share the same beam. Since the proposed
beam can be only shared by two users with different channel
qualities, it is probable to easily apply clustering and power
allocation algorithms to maximize the sum capacity and to
decrease the intercluster and interuser interferences. In [47],
performance of multicast beamforming, when the beam is
used to serve many users per cluster by sharing a common
signal, is investigated with superposition coding for a downlink MISO-NOMA network in a simple scenario of two users.
8
Principally, the transmitter of the BS has multiantenna and
its information stream is based on multiresolution broadcast
concept, in which only low priority signal is sent to the
user that is far away from the BS, that is, user with a
bad channel quality. Both signals of high priority and low
priority are transmitted to the user near to BS, that is, user
with good channel quality. Furthermore, with superposition
coding a minimum power beamforming problem has been
developed in order to find the beamforming vectors and
the powers for both users. Moreover, under the considered
optimization condition and the given normalized beamforming vectors (which are founded by an iterative algorithm),
the closed-form expression for optimal power allocation is
easily obtained. In [48], random beamforming is carried out
at the BS of a downlink MIMO-NOMA network. In the
system model, each beam is assumed to be used by all the
users in one cluster and all beams have similar transmission
power allocations. Moreover, a spatial filter is suggested to
be used in order to diminish the intercluster and interbeam
interferences. Fractional frequency reuse concept, in which
users with different channel conditions can accommodate
many reuse factors, is proposed in order to improve the power
allocation among multiple beams. In [49], interference minimization and capacity maximization for downlink multiuser
MIMO-NOMA system are introduced, in which the number
of receive antennas of mobile user is larger than the number
of transmit antennas of the BS. Zero-forcing beamforming
technique is suggested to reduce the intercluster interference,
especially when distinctive channel quality users is assumed.
In addition, dynamic power allocation and user-cluster algorithms have been proposed not only to achieve maximum
throughput, but also to minimize the interference.
There are many research works investigating resource
allocation problem in terms of maximization of the sum
rate in case of perfect CSI [50–52]. Specifically, in [50]
sum rate optimization problem of two-user MIMO-NOMA
network, that is, two users in one cluster in which different
precoders are implemented, has been introduced under the
constraint of transmission power at the BS and the minimum
transmission rate limitation of the user with bad channel
condition. In [51], the sum rate maximization problem for
downlink MISO-NOMA system is investigated. However, the
transmitted signal for each mobile user is weighted with
a complex vector. Moreover, for the sake of avoiding the
high computational complexity related to nonconvex optimization problem, minorization-maximization method is
suggested as an approximation. The key idea of minorizationmaximization algorithm is to design the complex weighting
vectors in such a way that the total throughput of the
system is maximized, for a given order of users; that is,
perfect CSI is assumed. In [52], a downlink MIMO-NOMA
system, where perfect CSI available at all nodes is assumed
and with different beams, BS broadcasts precoded signals
to all mobile users; that is, each beam serves several users.
However, there are three proposed algorithms combined in
order to maximize the sum rate. The first one is where
weighted sum rate maximization proposes to design a special
beamforming matrix of each beam benefiting from all CSI
at the BS. The second algorithm is where user scheduling
Wireless Communications and Mobile Computing
aims to have super SIC at the receiver of each mobile user.
Thus, to take full benefits of SIC, differences in channel
gains per cluster should be significant and the channel
correlation between mobile users has to be large. The final
one is where fixed power allocation targets optimization,
offering not only a higher sum rate, but also convenient
performance for the user with bad channel quality. In [53],
the optimal power allocation method, in order to maximize
the sum rate of two-user MIMO-NOMA with a layered
transmission scheme under a maximum transmission power
constraint for each mobile user, is investigated. Basically, by
using the layered transmission, each mobile user performs
sequence by sequence decoding signals throughout SIC,
yielding much lower decoding complexity when compared
to the case with nonlayered transmission. Moreover, the
closed-form expression for the average sum rate and its
bounds in both cases of perfect CSI and partial CSI are
obtained. Also, it is shown that the average sum rate is
linearly proportional to the number of antennas. In [54],
a comprehensive resource allocation method for multiuser
downlink MIMO-NOMA system including beamforming
and user selection is proposed, yielding low computational
complexity and high performance in cases of full and partial
CSI. However, resource allocation has been expressed in
terms of the maximum sum rate and the minimum of
maximum outage probability (OP) for full CSI and partial
CSI, respectively. Outage behavior for both downlink and
uplink networks in MIMO-NOMA framework with integrated alignment principles is investigated in a single cell
[55] and multicell [56, 57], respectively. Furthermore, an
appropriate trade-off between fairness and throughput has
been achieved by applying two strategies of power allocation methods. The fixed power allocation strategy realizes
different QoS requirements. On the other hand cognitive
radio inspired power allocation strategy verifies that QoS
requirements of the user are achieved immediately. In addition, exact and asymptotic expressions of the system OP
have been derived. In [58], the power minimization problem
for downlink MIMO-NOMA networks under full CSI and
channel distribution information scenarios are studied. In
[59], linear beamformers, that is, precoders that provide a
larger total sum throughput also improving throughput of
the user with bad quality channel, are designed; meanwhile
QoS specification requirements are satisfied. Also, it is shown
that the maximum number of users per cluster that realizes a
higher NOMA performance is achieved at larger distinctive
channel gains.
Moreover, since massive MIMO technologies can ensure
bountiful antenna diversity at a lower cost [4], many works
have discussed performance of NOMA over massive MIMO.
For instance, in [60], massive MIMO-NOMA system, where
the number of the transmit antennas at the BS is significantly
larger than the number of users, is studied with limited feedback. Also, the exact expressions of the OP and the diversity
order are obtained for the scenarios of perfect order of users
and one bit feedback, respectively. In [61], the scheme based
on interleave division multiple access and iterative data-aided
channel estimation is presented in order to solve the reliability
problem of multiuser massive MIMO-NOMA system with
Wireless Communications and Mobile Computing
imperfect CSI available at the BS. In [62], the achievable
rate in massive MIMO-NOMA systems and iterative dataaided channel estimation receiver, in which partially decoded
information is required to get a better channel estimation, are
investigated through applying two pilot schemes: orthogonal
pilot and superimposed pilot. However, pilots in the orthogonal pilot scheme occupy time/frequency slots while they are
superimposed with information in superimposed pilot one.
Moreover, it is shown that the greatest part of pilot power in
superimposed pilot scheme seems to be zero in the case when
Gaussian signal prohibits overhead power and rate loss that
may be resulted through using pilot. Consequently, with code
maximization superimposed scheme has a superior performance over orthogonal one under higher mobility and larger
number of mobile users. Different from massive MIMO,
in [63] performance of massive access MIMO systems, in
which number of users is larger than the number of antennas
employed at the BS, is studied. Low-complexity Gaussian
message specially passing iterative detection algorithm is
used and both its mean and variance precisely converge with
high speed to those concerned with the minimum mean
square error multiuser detection in [64].
In addition, NOMA has been proposed as a candidate
MA scheme integrated with beamspace MIMO in mmWave
communication systems, satisfying massive connectivity,
where the number of mobile users is much greater than the
number of radio frequency chains, and obtaining a better
performance in terms of spectrum and energy efficiency
[65]. Furthermore, a precoding scheme designed on zeroforcing (ZF) concept has been suggested in order to reduce
the interbeam interference. Moreover, iterative optimization
algorithm with dynamic power allocation scheme is proposed
to obtain a higher sum rate and lower complexity. In [66],
the optimization problem of energy efficiency for MIMONOMA systems with imperfect CSI at the BS over Rayleigh
fading channels is studied under specified limitations on
total transmission power and minimum sum rate of the
user of bad channel condition. However, two-user scheduling
schemes and power allocation scheme are presented in
[67] in order to maximize the energy efficiency. The user
scheduling schemes depend on the signal space alignment;
while one of them effectively deals with the multiple interference, the other one maximizes the multicollinearity among
users. On the other hand, power allocation scheme uses
a sequential convex approximation that roughly equalizes
the nonconvex problem by a set of convex problems iteratively, that is, in each iteration nonconvex constraints are
modified into their approximations in inner convex. Also,
it is shown that higher energy efficiency is obtained when
lower power is transmitted and a higher sum rate of center
users is obtained when maximum multicollinearity scheme is
employed.
Many other problems have been investigated in MIMONOMA systems. For example, in [68, 69], QoS optimization
problem is proposed for two-user MISO-NOMA system.
In particular, closed-form expressions of optimal precoding
vectors over flat fading channels, are achieved by applying the
Lagrange duality and an iterative method in [68] and [69],
respectively.
9
As mentioned before, NOMA promises to satisfy the
need of IoT, in which many users require to be served
rapidly for small packet transmissions. Consequently, the
literature tends to study performance of MIMO-NOMA for
IoT. For instance, in [70] a MIMO-NOMA downlink network
where one transmitter sending information to two users
is considered. However, one user has a low data rate, that
is, small packet transmission, while the second user has a
higher rate. Particularly, outage performance in case of using
precoding and power allocation method is investigated. Also,
it is shown that the potential of NOMA is apparent even when
channel qualities of users are similar.
Most current works of MIMO-NOMA focus on sum rate
and capacity optimization problems. However, performance
of symbol error rate (SER) for wireless communication
systems is also very substantial. In [71], SER performance
using the minimum Euclidean distance precoding scheme in
MIMO-NOMA networks is studied. For simple transmission
case, two-user 2 × 2 MIMO-NOMA is investigated. However, to facilitate realization of practical case of multiuser
MIMO-NOMA network, two-user pairing algorithms are
applied.
In order to demonstrate the significant performance
of MIMO-NOMA systems in terms of both OP and sum
rate, as well as its superiority over MIMO-OMA, a special
case, performance of single input multiple output- (SIMO-)
NOMA network based on maximal ratio combining (MRC)
diversity technique in terms of both OP and ergodic sum
rate is investigated in the following section. Moreover, closedform expression of OP and bounds of ergodic sum rate are
derived.
3.1. Performance Analysis of SIMO-NOMA. This network
includes a BS and 𝐿 mobile users as shown in Figure 5. The
transmitter of BS is equipped with a single antenna and the
receiver of each mobile user is equipped with 𝑁𝑟 antennas.
The received signal at the 𝑙th user after applying MRC can be
written as follows:
𝐿
hH
󵄩 󵄩
𝑟𝑙 = 󵄩󵄩󵄩hl 󵄩󵄩󵄩 ∑√𝑎𝑖 𝑃𝑠 𝑥𝑖 + 󵄩󵄩 l 󵄩󵄩 nl ,
󵄩󵄩hl 󵄩󵄩
𝑖=1
(21)
where hl is 𝑁𝑟 × 1 fading channel coefficient vector between
the BS and 𝑙th user and without loss of generality and due
to NOMA concept they are sorted in ascending way; that is,
‖h1 ‖2 ≤ ‖h2 ‖2 ≤ ⋅ ⋅ ⋅ ≤ ‖hL ‖2 , and nl is 𝑁𝑟 × 1 zero mean
2
complex additive Gaussian noise with 𝐸[nl nH
l ] = I𝑁𝑟 𝜎𝑙 at
the 𝑙th user, where 𝐸[⋅], (⋅)𝐻, and I𝑟 denote the expectation
operator, Hermitian transpose, and identity matrix of order 𝑟,
respectively, and 𝜎𝑙2 = 𝜎2 is the variance of nl per dimension.
From (21), instantaneous SINR for 𝑙th user to detect 𝑗th user,
𝑗 ≤ 𝑙, with 𝑗 ≠ 𝐿 can be expressed as follows:
SINR𝑗→𝑙 =
󵄩 󵄩2
𝑎𝑗 𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩
.
󵄩 󵄩2
𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩 ∑𝐿𝑖=𝑗+1 𝑎𝑖 + 1
(22)
10
Wireless Communications and Mobile Computing
h
U1
Nr
hl
Ul
Base station
BS
Nr
hL
UL
Nr
Figure 5: System model of the downlink SIMO-NOMA.
Now, nonordered channel gains for MRC can be given as
follows:
̃ ‖2 ] and 𝜗 (𝑏, 𝑔 ) denotes multinomial
where Ω = 𝐸[‖h
l
𝑎
𝑐
coefficients which can be defined as [72, eq. (0.314)]
𝑁
𝑟
󵄩󵄩 ̃ 󵄩󵄩2
󵄩󵄩hl 󵄩󵄩 = ∑ 󵄨󵄨󵄨󵄨ℎ𝑙,𝑖 󵄨󵄨󵄨󵄨2 , 𝑙 = 1, 2, . . . , 𝐿,
󵄩 󵄩
(23)
𝑖=1
where ℎ𝑙,𝑖 denotes the channel coefficient between the BS
and 𝑖th antenna of the 𝑙th user and are independent and
identically distributed (i.i.d.) Nakagami-𝑚 random variables.
By the help of the series expansion of incomplete Gamma
function [72, eq. (8.352.6)], the cumulative distribution
function (CDF) and probability density function (PDF) of
Gamma random variable 𝑋, square of Nakagami-𝑚 random
variable can be defined as follows:
𝐹𝑋 (𝑥) =
𝑚−1
𝛾 (𝑚, 𝑚𝑥/Ω)
𝑚𝑥 𝑘 1
= 1 − 𝑒−𝑚𝑥/Ω ∑ (
)
,
Γ (𝑚)
Ω
𝑘!
𝑘=0
𝑓𝑋 (𝑥) = (
𝑚 𝑚 𝑥𝑚−1 −𝑚𝑥/Ω
,
)
𝑒
Ω
Γ (𝑚)
(24)
𝛾 (𝑚𝑁𝑟 , 𝑚𝑥/Ω)
Γ (𝑚𝑁𝑟 )
−𝑚𝑥/Ω
=1−𝑒
1 𝑟(𝑚𝑁𝑟 −1)
=∑
∑
𝑟=0
𝑠=0
(−1)𝑟 𝜗𝑠 (𝑟, 𝑚𝑁𝑟 ) 𝑥𝑠 𝑒−𝑟𝑚𝑥/Ω ,
(25)
(26)
𝑎 ≥ 1.
In (26), 𝑑𝜌 = (𝑔𝑐 /Ω)𝜌 /𝜌!, 𝜗0 (𝑏, 𝑔𝑐 ) = 1, and 𝜗𝑎 (𝑏, 𝑔𝑐 ) = 0 if
𝜌 > 𝑔𝑐 − 1. Next, CDF of the ordered ‖hl ‖2 can be expressed
as [74]
𝐹‖hl ‖2 (𝑥) =
𝐿−𝑙
𝐿!
(−1)𝑡 𝐿 − 𝑙
(
∑
)
(𝐿 − 𝑙)! (𝑙 − 1)! 𝑡=0 𝑙 + 𝑡
𝑡
× [𝐹‖h̃l ‖2 (𝑥)]
𝑙+𝑡
⋅∑∑
∑
𝑡=0 𝑟=0
𝑠=0
=
𝐿!
(𝐿 − 𝑙)! (𝑙 − 1)!
(27)
(−1)𝑡+𝑟
𝑙+𝑡
𝐿−𝑙
𝑙+𝑡
⋅(
)(
) 𝜗𝑠 (𝑟, 𝑚𝑁𝑟 ) 𝑥𝑠 𝑒−𝑟𝑚𝑥/Ω .
𝑡
𝑟
3.1.1. Outage Probability of SIMO-NOMA. The OP of the 𝑙th
user can be obtained as follows:
𝑃out,𝑙 = Pr (SINR𝑗→𝑙 < 𝛾th𝑗 )
𝑚𝑁𝑟 −1
𝑚𝑥 𝑠 1
)
∑ (
Ω
𝑠!
𝑠=0
1 𝑎
∑ (𝜌 (𝑏 + 1) − 𝑎) 𝑑𝜌 𝜗𝑎−𝑏 (𝑏, 𝑔𝑐 ) ,
𝑎𝑑0 𝜌=1
𝐿−𝑙 𝑙+𝑡 𝑟(𝑚𝑁𝑟 −1)
where 𝛾(⋅, ⋅) and Γ(⋅) are the lower incomplete Gamma
function given by [72, eq. (8.350.1)] and the Gamma function
given by [72, eq. (8.310.1)], respectively. 𝑚 is parameter of
Nakagami-𝑚 distribution, and Ω = 𝐸[|𝑋|2 ]. With the help
of the highest order statistics [73], we can write CDF of
̃ ‖2 as follows:
nonordered ‖h
l
𝐹‖h̃l ‖2 (𝑥) =
𝜗𝑎 (𝑏, 𝑔𝑐 ) =
󵄩 󵄩2
𝑎𝑗 𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩
< 𝛾th𝑗 )
= Pr ( 󵄩 󵄩2 𝐿
𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩 ∑𝑖=𝑙+1 𝑎𝑖 + 1
󵄩 󵄩2
= Pr (󵄩󵄩󵄩hl 󵄩󵄩󵄩 <
𝛾th𝑗
𝛾 (𝑎𝑗 − 𝛾th𝑗 ∑𝐿𝑖=𝑙+1 𝑎𝑖 )
)
Wireless Communications and Mobile Computing
󵄩 󵄩2
= Pr (󵄩󵄩󵄩hl 󵄩󵄩󵄩 < 𝜂𝑙∗ ) = 𝐹‖hl ‖2 (𝜂𝑙∗ ) =
𝐿−𝑙 𝑙+𝑡 𝑟(𝑚𝑁𝑟 −1)
⋅∑∑
∑
𝑡=0 𝑟=0
𝑠=0
11
𝐿!
(𝐿 − 𝑙)! (𝑙 − 1)!
(−1)𝑡+𝑟
𝑙+𝑡
∞
1
∫ ln (1 + 𝛼𝐿 𝛾𝑥) 𝑓‖hL ‖2 (𝑥) 𝑑𝑥
2 ln 2 0
=
𝑎𝐿 𝛾 ∞ 1 − 𝐹‖hL ‖2 (𝑥)
𝑑𝑥,
∫
2 ln 2 0
1 + 𝑎𝐿 𝛾𝑥
(32)
𝐿−𝑙
𝑙+𝑡
𝑠
∗
⋅(
)(
) 𝜗𝑠 (𝑟, 𝑚𝑁𝑟 ) 𝜂𝑙∗ 𝑒−𝑟𝑚𝜂𝑙 /Ω ,
𝑡
𝑟
Simply, by using (27) 𝐹‖hL ‖2 can be expressed as
(28)
where 𝜂𝑙∗ = max[𝜂1 , 𝜂2 , . . . , 𝜂𝑙 ] with 𝜂𝑗 = 𝛾th𝑗 /𝛾(𝑎𝑗 −
𝛾th𝑗 ∑𝐿𝑖=𝑙+1 𝑎𝑖 ). 𝛾th𝑗
=
𝐹‖hL ‖2 (𝑥)
=1
denotes the threshold SINR of the 𝑗th user.
Under the condition 𝑎𝑗 > 𝛾th𝑗 ∑𝐿𝑖=𝑗+1 𝑎𝑖 , the 𝑙th user can
decode the 𝑗th user’s signal successfully irrespective of the
channel SNR.
3.1.2. Ergodic Sum Rate Analysis of SIMO-NOMA. Ergodic
sum rate can be expressed as
𝐿 𝑘(𝑚𝑁𝑟 −1)
+∑
∑
𝑘=1
𝑛=0
𝑅𝐿 =
1
𝑅sum = ∑𝐸 [ log2 (1 + SINR𝑙 )]
2
𝑙=1
𝑘(𝑚𝑁𝑟 −1)
𝑎𝐿 𝛾 𝐿
∑
2 ln 2 𝑘=1
𝑛=0
𝐼
(29)
By defining 𝑢 = 𝑎𝐿 𝛾𝑥, 𝐼 can be written as follows:
𝑅𝐿
𝐼=
1
+ 𝐸 [ log2 (1 + SINR𝐿 )].
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
2
𝑛−1
(𝑎𝐿 𝛾)
∫
0
𝑢𝑛 𝑒−𝑘𝑚𝑢/𝑎𝐿 𝛾Ω
𝑑𝑢.
1+𝑢
ln (𝑎𝐿 𝛾Ω/𝑚𝑘)
{
,
{
{
𝑎𝐿 𝛾
𝐼≈𝜉={
𝑛
{
{ Γ (𝑛) (Ω/𝑚𝑘) ,
𝑎𝐿 𝛾
{
Then, 𝑅𝐿 can be expressed as
󵄩 󵄩2
𝐿−1
𝑎𝑙 𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩
1
𝑅𝐿 = ∑ 𝐸 [ log2 (1 + 󵄩 󵄩2 𝐿
)]
2
𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩 ∑𝑖=𝑙+1 𝑎𝑖 + 1
𝑙=1
(30)
𝐿−1
𝑎𝑙
1
= ∑ 𝐸 [ log2 (1 + 𝐿
󵄩 󵄩2 )] .
2
∑𝑖=𝑙+1 𝑎𝑖 + 1/𝛾 󵄩󵄩󵄩hl 󵄩󵄩󵄩
𝑙=1
(35)
𝑎
1 𝐿−1
∑ log2 (1 + 𝐿 𝑙 ) .
2 𝑙=1
∑𝑖=𝑙+1 𝑎𝑖
(31)
∞
Now, by using the identity ∫0 ln(1 + 𝑎𝑦)𝑓(𝑦)𝑑𝑦 = 𝑎 ∫0 ((1 −
𝐹(𝑦))/(1 + 𝑎𝑦))𝑑𝑦, log𝑏 𝑎 = ln 𝑎/ln 𝑏, 𝑅𝐿 can be written as
𝑛=0
(36)
𝑛 > 0.
By substituting (36) into (34), then 𝑅𝐿∞ can be given by
𝑅𝐿∞ =
Due to computational difficulty of calculating the exact
expression of the ergodic sum rate, and, for the sake of
simplicity, we will apply high SNR analysis in order to find
the upper and lower bounds related to ergodic sum rate. Thus,
when 𝛾 → ∞ in (30), then 𝑅𝐿∞ can be given by
1
󵄩 󵄩2
𝐸 [ln (1 + 𝑎𝐿 𝛾 󵄩󵄩󵄩hL 󵄩󵄩󵄩 )]
2 ln 2
∞
1
Using [74, (eq. 11)], as 𝛾 → ∞, then 𝐼 can be approximated as
𝑅𝐿
=
(34)
∞ 𝑛 −𝑘𝑚𝑥/Ω
𝑥 𝑒
𝑑𝑥.
⋅∫
1 + 𝑎𝐿 𝛾𝑥
0
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
1
= ∑ 𝐸 [ log2 (1 + SINR𝑙 )]
2
𝑙=1
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
1
󵄩 󵄩2
𝑅𝐿 = 𝐸 [ log2 (1 + 𝑎𝐿 𝛾 󵄩󵄩󵄩hL 󵄩󵄩󵄩 )]
2
𝐿
( ) (−1)𝑘+1 𝜗𝑛 (𝑘, 𝑚𝑁𝑟 )
𝑘
∑
𝐿−1
∞
( ) (−1)𝑘 𝜗𝑛 (𝑘, 𝑚𝑁𝑟 ) 𝑥𝑛 𝑒−𝑘𝑚𝑥/Ω .
𝑘
By substituting (33) into (32),
𝐿
𝑅𝐿∞ =
(33)
𝐿
𝑎𝐿 𝛾 𝐿
∑
2 ln 2 𝑘=1
𝑘(𝑚𝑁𝑟 −1)
∑
𝑛=0
𝐿
( ) (−1)𝑘+1 𝜗𝑛 (𝑘, 𝑚𝑁𝑟 ) 𝜉.
𝑘
(37)
Finally, by substituting (37) and (31) into (29), then asymp∞
totic ergodic sum rate 𝑅sum
can be expressed as
∞
𝑅sum
=
𝑎
1 𝐿−1
∑ log (1 + 𝐿 𝑙 )
2 𝑙=1 2
∑𝑖=𝑙+1 𝑎𝑖
+
𝑎𝐿 𝛾 𝐿
∑
2 ln 2 𝑘=1
𝑘(𝑚𝑁𝑟 −1)
∑
𝑛=0
(38)
𝐿
( ) (−1)𝑘+1 𝜗𝑛 (𝑘, 𝑚𝑁𝑟 ) 𝜉.
𝑘
3.1.3. Numerical Results of SIMO-NOMA. We consider two
users and their average power factors that provide ∑𝐿𝑖=1 𝑎𝑖 = 1
are selected as 𝑎1 = 0.6 and 𝑎2 = 0.4, respectively. Also,
in order to make a comparison between the performances
12
Wireless Communications and Mobile Computing
100
considers the signal of the second user as noise, while ergodic
rate for the second user proportionally increases with SNR
because of no interference with the first one. Figures 6 and 7
show that NOMA outperforms conventional OMA in terms
of outage probability and ergodic sum rate, respectively.
(m, Nr ) = (2, 2)
Outage probability
10−1
10−2
4. Cooperative NOMA
10−3
(m, Nr ) = (2, 4)
10−4
0
2
4
6
8
10
SNR (dB)
Simulation: U1
Simulation: U2
Exact
12
14
16
Conventional OMA
Figure 6: Outage probability of MIMO-NOMA system versus SNR
for 𝐿 = 2, 𝑎1 = 0.6, 𝑎2 = 0.4, 𝛾th1 = 1, 𝛾th2 = 2, and 𝛾th = 5.
4.5
4
Sum rate (bps/Hz)
3.5
3
2.5
2
1.5
1
0.5
0
0
2
4
Rate: U1
Rate: U2
Sum rate
6
8
10 12
SNR (dB)
14
16
18
20
Lower bound sum rate
Upper bound sum rate
Conventional OMA
Figure 7: Ergodic sum rate of MIMO-NOMA system versus SNR
for 𝐿 = 2, 𝑎1 = 0.6, 𝑎2 = 0.4, 𝛾th1 = 1, 𝛾th2 = 2, 𝛾th = 5, and
(𝑚, 𝑁𝑟 ) = (2, 2).
of conventional OMA and the proposed NOMA in terms of
OP and ergodic sum rate over Nakagami-𝑚 fading channels,
SNR threshold value of conventional OMA 𝛾th , which verifies
(1/2) ∑𝐿𝑖=1 log2 (1 + 𝛾th𝑖 ) = (1/2)log2 (1 + 𝛾th ), is used.
Figure 6 shows the outage probability versus the system
SNR over different Nakagami m parameters. In Figure 6, the
simulations verify exact analytical results and a better outage
performance at higher number of antennas is obtained.
Figure 7 depicts the ergodic sum rates of mobile users
versus the system SNR. It is observed that ergodic rate for
the first user is approximately constant over high SNR. This
is due to high power allocation for the first user, such that it
Cooperative communication, where the transmission between the source and destination is maintained by the help
of one or multiple relays, has received significant attention of
researchers since it extends the coverage area and increases
system capacity while reducing the performance deteriorating effects of multipath fading [75, 76]. In cooperative communication systems, relays transmit the received information
signals to the related destinations by applying forwarding
protocols, such as amplify-and-forward (AF) and decodeand-forward (DF). In addition, in the last decade, the relays
can be fundamentally categorized as half-duplex (HD) and
full-duplex (FD) according to relaying operation. Differing
from HD, FD relay maintains the data reception and transmission process simultaneously in the same frequency band
and time slot [77]. Thus, FD relay can increase the spectral
efficiency compared to its counterpart HD [78]. Therefore,
the combination of cooperative communication and NOMA
has been considered as a remarkable solution to further
enhance the system efficiency of NOMA. Accordingly, in
[79], a cooperative transmission scheme, where the users with
stronger channel conditions are considered as relays due to
their ability in the decoding information of other users in
order to assist the users with poor channel conditions, has
been proposed to be implemented in NOMA. In [80], by
assuming the same scenario in [79], Kim et al. proposed a
device-to-device aided cooperative NOMA system, where the
direct link is available between the BS and one user, and
an upper bound related to sum capacity scaling is derived.
In addition, a new power allocation scheme is proposed
to maximize the sum capacity. On the other hand, in [81],
the authors analyze the performance of NOMA based on
user cooperation, in which relaying is realized by one of the
users, operating in FD mode to provide high throughput, by
applying power allocation.
However, aforementioned user cooperation schemes are
more appropriate for short-range communications, such as
ultrawideband and Bluetooth. Therefore, in order to further
extend the coverage area and to exploit the advantages of
cooperation techniques, the concept of cooperative communication, where dedicated relays are used, has also been
investigated in NOMA. In this context, in [82], a coordinated
transmission protocol where a user communicates with BS
directly while the other needs the help of a relay to receive
the transmitted information from the BS has been employed
in NOMA scheme in order to improve the spectral efficiency,
and OP analysis is conducted for frequency-flat block fading
channels by using DF relaying, as shown in Figure 8(a). In
[83], the same scenario in [82] is considered, and OP and
asymptotic expressions are obtained in approximated closed
forms for AF relaying networks. Differing from [82] and
[83], in [84], the authors proposed a cooperative relaying
Wireless Communications and Mobile Computing
13
ℎRU1
ℎSR
Relay
(R)
Base
station
(BS)
U2
Base
station
(BS)
Relay
(R)
ℎRU
U1
Ul
ℎRU
U1
1st phase
2nd phase
UL
1st phase
2nd phase
(a)
(b)
Figure 8: System model of cooperative NOMA downlink. (a) Coordinated direct and relay transmission. (b) A cooperative scheme without
direct link.
system, where two symbols transmitted from the BS to the
user by the help of a relay were combined at the BS by applying NOMA concept. The exact and asymptotic expressions
related to achievable average rate are derived in i.i.d. Rayleigh
fading channels and the results demonstrate that cooperative
relaying based on NOMA outperforms the conventional one.
Also, the authors of [85] analyzed the same transmission
scheme in [84] over Rician fading channels. In order to
further improve the achievable rate of the system investigated
in [84], in [86], authors proposed a novel receiver scheme,
where the transmitted symbols from the BS are combined at
the destination according to MRC technique and investigated
the system performance in terms of ergodic sum rate and OP.
Their results demonstrate that the proposed scheme achieves
better performance than the one in [84]. In addition, Wan
et al. [87] investigated the same system in [86] by using
two DF relays and assuming no direct link for cooperation
and analyzed the system performance in terms of achievable
sum rate. In [88], the authors investigate the performance
of NOMA over i.i.d. Rayleigh fading channels by employing
a downlink cooperative network in which the BS transmits
the superimposed information to the mobile users through a
relay and also the direct link is considered. The OP expression
of the related user is obtained in closed form, and ergodic sum
rate and asymptotic analyses are also maintained as performance metrics. The results show that the NOMA exhibits the
same performance in terms of diversity order when compared
to OMA by improving spectral efficiency and providing a
better user fairness. Furthermore, in [89], performance of
NOMA is investigated in relaying networks without the direct
link over Nakagami-𝑚 fading environments for the network
given in Figure 8(b) where all nodes and mobile users are
assumed to have a single antenna. While closed-form OP
expressions and simple bounds are obtained, ergodic sum rate
and asymptotic analyses are also conducted. Under the consideration of imperfect CSI, the authors of [90] analyze the
performance of NOMA system investigated in [89] in terms
of OP. They provide exact OP and lower bound expressions in
closed form and their results show that an error floor comes
up due to the imperfect CSI at all SNR region. Similar to
the scenario in [89], in [91], performance of NOMA with
fixed gain AF relaying is analyzed over Nakagami-𝑚 fading
channels in case when the direct transmission also exists. For
performance criterion, new closed-form expressions related
to the exact and asymptotic OPs are obtained. Moreover, a
buffer-aided cooperative technique, where the relay transmits
and receives the information packets when source-relay
and relay-destination links are in outage, respectively, has
been taken into account by researchers in order to further
enhance the reliability of the relaying systems and increase
the system throughput [92]. Accordingly, in [93], the authors
proposed a cooperative NOMA system with buffer-aided
relaying technique consisting of one source and two users
in which the stronger user is used as a buffer-aided relay.
Differing from [93], Zhang et al. [94] proposed a buffer-aided
NOMA relay network in which a dedicated relay was used to
forward the information to two users, and exact OP of the
system was obtained in single integral form and lower/upper
bounds were derived in closed forms. In [95], for the same
system in [94], an adaptive transmission scheme in which
the working mode is adaptively chosen in each time slot is
proposed to maximize the sum throughput of the considered
NOMA system.
As can be seen from the aforementioned studies, the
power allocation issue is vital for the performances of user
destinations. In this context, there are several studies that
focus on power allocation strategies for cooperative NOMA
in the literature [96–99]. Accordingly, in [96], the authors
proposed a novel two-stage power allocation scheme for
cooperative NOMA with direct link consisting of one source,
one relay, and one user destination in order to improve sum
rate and OP of the system. In [97], Gau et al. proposed a novel
dynamic algorithm that selects the optimal relaying mode
and determines the optimal power allocation for cooperative
NOMA, where the BS communicates with two users via a
couple of dedicated relays. For the proposed approach, new
closed-form expressions related to optimal power allocation
were derived. In [98], the authors investigated a joint subcarrier pairing and power allocation problem in cooperative
NOMA which consists of one BS and two users (one of the
users acts as a relay). Theoretical expressions related to joint
14
optimization approach are derived and superiority of the considered algorithms is demonstrated by simulations. In [99],
in order to optimize the resource allocation for maximizing
the average sum-rate, authors studied the performance of
a single-cell NOMA system consisting of multiple sourcedestination pairs and one OFDM AF relay.
As well known from the literature, diversity techniques
and using multiantenna strategies improve system performance significantly. Therefore, in [100], the same authors
of [88] consider using multiple antennas at the BS and
mobile users and analyze the OP behavior of the network
over i.i.d. Rayleigh in case when the direct link does not
exist. They apply TAS and MRC techniques at the BS and
mobile users, respectively, while the relay has single antenna
and show that using multiple antennas improves the system
OP performance. Additionally, it is shown that NOMA
provides a better OP performance than OMA when the
distance between the BS and relay is sufficiently short. In
[101], OP performance of the same system investigated in
[100] was analyzed for Nakagami-𝑚 channels in case that
fixed gain AF relay was used. In [102], performance of
the same system in [100] was investigated over Nakagami𝑚 fading environments in the presence of imperfect CSI.
The system OP was obtained in closed form and tight
lower/upper bounds were provided for further insights. In
[103], the authors proposed an Alamouti space-time block
coding scheme based on two-phase cooperative DF relaying
for NOMA and obtained closed-form expressions for both
OP and ergodic sum-rate. In [104], the authors analyzed
the system performance of nonregenerative massive MIMO
NOMA relay network in case that SIC and maximum mean
square error SIC techniques were adopted at the receivers. In
the system, multiple users and relays are equipped with single
antenna while the BS has multiple antennas. For performance
metrics, system capacity and sum rate expressions were
derived in closed forms and authors demonstrated that the
considered system outperforms massive MIMO OMA.
In addition to the aforementioned studies, using multirelays and/or relay selection techniques in cooperative NOMA
concept are hot issues since using multiple relays improves
the system performance significantly as already known from
studies in the literature. Therefore, in [105], the authors
proposed a novel NOMA relaying system based on hybrid
relaying scheme, where some of relays adopted DF protocol
while the others used AF for signal transmission, consisting
of two sources and one user destination. For performance
comparison with the conventional systems, channel capacity
and average system throughput were investigated, and the
proposed system was shown to achieve larger sum channel
capacity and average system throughput than the conventional systems. Gendia et al. [106] investigated a cooperative
NOMA with multiple relays in which all users except the user
to whom the information signal would be transmitted were
considered as relays. Comparisons with the other equivalent
NOMA systems were done in terms of user-average bit error
rate, ergodic sum rate, and fairness level by simulations. In
[107], OP performance of a NOMA system, where the BS
transmits the information signals to two users by using two
relays, was analyzed when cooperative and TDMA schemes
Wireless Communications and Mobile Computing
were applied for transmission. The authors demonstrated
that cooperative scheme outperforms TDMA one in terms
of OP. Shin et al. [108] proposed a novel multiple-relayaided uplink NOMA scheme for multicell cellular networks
where the BS was equipped with multiantenna and limited by user numbers in each cell. Moreover, the feasibility conditions of the considered system were investigated.
Besides multirelaying strategies, relay selection techniques
were also investigated. Accordingly, in [109], the authors
investigated the impact of two relay selection techniques
on the performance of cooperative NOMA scheme without
direct link. According to the results, with the relay selection
strategies significant performance gain in terms of OP has
been achieved in NOMA compared to counterpart OMA.
In [110], performance of a cooperative NOMA with the best
relay selection technique was analyzed in terms of average
rate. The considered relay network consists of one BS, one
user, and multiple relays and the direct link is also available.
Authors demonstrated that the significant performance gain
can be achieved by increasing the number of relays when
compared to OMA one. Deng et al. [111] investigated the
joint user and relay selection problem in cooperative NOMA
relay networks, where multiple source users communicate
with two destination users via multiple AF relays. In order
to improve the system performance, the authors proposed an
optimal relay selection scheme, where the best user-relay pair
was selected. In [112], performance of cooperative NOMA
with AF relays was analyzed by using partial relay selection
technique. In the network, communication between the BS
and two users was realized by selected relay, and also direct
link between the BS and users was taken into account. While
authors provided closed-form OP and sum rate expressions,
asymptotic analysis at high SNR region was also conducted. It
is shown that the performance can be improved by increasing
the number of relays, but the same performance gain is
obtained at high SNR region for more than two relays. In
addition to above studies, Yang et al. [113] proposed a novel
two-stage relay selection scheme for NOMA networks which
consists of one source, multiple DF/AF relays, and two users.
The considered selection strategy relies on satisfying the QoS
of one user in the first stage while maximizing the rate of the
other user in the second stage.
Besides that NOMA improves the system spectral efficiency, energy harvesting (EH) technology has also gained
much attention because of its ability in increasing energy
efficiency. Therefore, simultaneous wireless information and
power transfer (SWIPT), which uses radio-frequency signals
to enable self-sustainable communication, was proposed
by Varshney [114] and regarded as an efficient solution
over all emerging EH techniques due to the limitation of
environmental energy sources. In this context, many studies
combining cooperative NOMA with EH technologies were
conducted in the literature [115–123]. In order to exploit
the energy and spectral efficiency features of SWIPT and
NOMA, Liu et al. [115] studied the application of SWIPT
to cooperative NOMA, where users nearby to the BS act as
EH relays. In addition, different user selection schemes were
proposed in order to determine which nearby user would
Wireless Communications and Mobile Computing
cooperate with far user, and OP and throughput expressions
related to the selection schemes were obtained in closed
forms. In [116], a transceiver design problem in cooperative
NOMA with SWIPT was studied. In the considered system,
the stronger user acting as a relay and BS were equipped
with multiple antennas while the other user had only single
antenna. Optimal transmitter beamforming and ZF-based
transmitter beamforming structures were proposed to maximize the rate of relay node. In [117, 118], the authors analyzed
OP performance of NOMA-SWIPT relay networks over i.i.d.
Rayleigh and Nakagami-𝑚 fading environments, respectively.
Differing from the previous works, authors considered that
the BS and multiple users were equipped with multiple
antennas and communication between the BS and users was
established only via an EH relay. They considered that TAS
and MRC techniques were employed at the BS and users,
respectively, and proved closed-form OP expressions for
performance criterion. Similar to [115], in [119], a best-near
best-far user selection scheme was proposed for a cellular
cooperative NOMA-SWIPT system and OP analysis was
conducted to demonstrate the superiority of the proposed
scheme. In [120], the authors investigated TAS schemes in
MISO-NOMA system based on SWIPT technique, where
the BS with multiple antennas communicates with two users
with single antenna and the stronger user is also used as an
EH relay, in terms of OP and conducted diversity analysis.
The impact of power allocation on cooperative NOMASWIPT networks was investigated by Yang et al. [121]. For
performance comparisons with existing works, OP and high
SNR analyses were conducted, and the proposed system was
shown to improve the OP performance significantly. In [122],
authors analyzed OP performance of a downlink NOMA with
EH technique consisting of one BS and two users. While
the BS and one of the users which was used as a relay were
equipped with multiple antennas, the other user far from
the BS had only single antenna. Closed-form OP expressions
were derived for AF, DF, and quantize-map-forward relaying
protocols over i.i.d. Rayleigh fading channels. Xu et al. [123]
investigated joint beamforming and power splitting control
problem in NOMA-SWIPT system studied in [120]. In order
to maximize the rate of the relay user, power splitting ratio
and beamforming vectors were optimized. Moreover, SISONOMA system was also studied.
While most of the prior works on the cooperative NOMA
systems have focused on the use of HD relaying technique,
there are also some studies that consider using FD relaying
technique in order to further increase spectral efficiency of
NOMA systems. In [124], performance of cooperative SISONOMA relaying system consisting of one BS and two users
was investigated. The user near BS was considered as an
FD relay which employed compress-and-forward protocol
for poor user. Authors provided theoretical expressions of
achievable rate region based on the noisy network coding.
Zhong and Zhang [125] proposed using FD relay instead of
HD for the investigated system in [82], where one user can
communicate with the BS directly while the other needs a
relay cooperation. In order to demonstrate the superiority
of using FD relay, authors provided exact OP and ergodic
15
sum capacity expressions. In [126], OP performance of
cooperative NOMA system in which the strong user helps
the other by acting as an FD-DF relay was analyzed in terms
of OP. Moreover, an adaptive multiple access scheme that
selects access mode between proposed NOMA, conventional
NOMA, and OMA was investigated in order to further
enhance the system OP. Differing from [126], authors of
[127] investigated optimizing the maximum achievable rate
region of cooperative NOMA system in which the BS also
operated in FD mode. Therefore, the authors proposed three
approaches for maximization problem, such as fixed transmit power, nonfixed transmit power, and transmit power
corrupted by error vector magnitude. In [128], a hybrid
half/full-duplex relaying scheme was proposed to implement
in cooperative NOMA and power allocation problem was
investigated in terms of achievable rate. In addition, NOMA
with HD and NOMA with FD systems were separately
investigated by providing closed-form optimal expressions
related to powers. Hybrid NOMA scheme was shown to
outperform the other NOMA schemes. The same hybrid
NOMA system in [128] was also investigated by Yue et al.
[129] in terms of OP, ergodic rate, and energy efficiency. In
addition, the authors also investigated the system when the
direct link was not available between the BS and poor user. In
[130], OP and ergodic sum rate performance of a cooperative
NOMA system with FD relaying was investigated in case that
the direct link was not available. Theoretical expressions were
derived in closed forms. Moreover, in order to maximize the
minimum achievable rate, optimization problem for power
allocation was also studied.
In the next section, we provide an overview of the
cooperative NOMA system which is investigated in [89] to
provide an example of cooperative NOMA.
4.1. Performance Analysis of Cooperative NOMA. Consider a
dual hop relay network based on downlink NOMA as given in
Figure 8(b) which consists of one BS (𝑆), one AF HD relay (𝑅),
and 𝐿 mobile users. In the network, all nodes are equipped
with a single antenna, and direct links between the BS and
mobile users can not be established due to the poor channel
conditions and/or the mobile users are out of the range of
BS. We assume that all channel links are subjected to flat
Nakagami-𝑚 fading. Therefore, channel coefficients of 𝑆-𝑅
and 𝑅-𝑈𝑙 are denoted by ℎ𝑆𝑅 and ℎ𝑅𝑈𝑙 with the corresponding
squared means 𝐸[|ℎ𝑆𝑅 |2 ] = Ω𝑆𝑅 and 𝐸[|ℎ𝑅𝑈|2 ] = Ω𝑅𝑈,
respectively, where 𝑙 = 1, . . . , 𝐿. In order to process NOMA
concept, without loss of generality, we consider ordering the
channel gains of 𝐿 users as |ℎ𝑅𝑈1 |2 ≤ |ℎ𝑅𝑈2 |2 ≤ ⋅ ⋅ ⋅ ≤ |ℎ𝑅𝑈𝐿 |2 .
In the first phase, the superimposed signal 𝑠 given in (1) is
transmitted from the BS to the relay and then the received
signal at 𝑅 can be modeled as
𝐿
𝑦𝑅 = ℎ𝑆𝑅 ∑√𝑎𝑖 𝑃𝑠 𝑥𝑖 + 𝑛𝑅 ,
(39)
𝑖=1
where 𝑛𝑅 is the complex additive Gaussian noise at 𝑅 and
distributed as CN(0, 𝜎𝑅2 ).
16
Wireless Communications and Mobile Computing
In the second phase, after the relay applies AF protocol,
the received signal at 𝑈𝑙 can be written as
𝐿
𝑦𝑅𝑈𝑙 = √𝑃𝑅 𝐺ℎ𝑆𝑅 ℎ𝑅𝑈𝑙 ∑√𝑎𝑖 𝑃𝑠 𝑥𝑖 + √𝑃𝑅 𝐺ℎ𝑅𝑈𝑙 𝑛𝑅
𝑖=1
𝑃out,𝑙 = 1
(40)
+ 𝑛𝑈𝑙 ,
where 𝑛𝑈𝑙 is the complex additive Gaussian noise at 𝑈𝑙 and
distributed as CN(0, 𝜎𝑈2 𝑙 ), and 𝑃𝑅 is the transmit power at 𝑅.
𝐺 denotes the amplifying factor and can be chosen as
(41)
󵄨2
󵄨 󵄨2 󵄨
𝑎𝑙 𝛾2 󵄨󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 󵄨󵄨󵄨󵄨ℎ𝑅𝑈𝑙 󵄨󵄨󵄨󵄨
, (42)
=
󵄨2
󵄨2
󵄨 󵄨2 󵄨
󵄨 󵄨2 󵄨
𝛾2 󵄨󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 󵄨󵄨󵄨󵄨ℎ𝑅𝑈𝑙 󵄨󵄨󵄨󵄨 Ψ𝑙 + 𝛾 (󵄨󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 + 󵄨󵄨󵄨󵄨ℎ𝑅𝑈𝑙 󵄨󵄨󵄨󵄨 ) + 1
where Ψ𝑙 = ∑𝐿𝑖=𝑙+1 𝑎𝑖 . Then, the received SINR by the 𝐿th user
can be simply expressed as [89]
󵄨2
󵄨 󵄨2 󵄨
𝑎𝐿 𝛾2 󵄨󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 󵄨󵄨󵄨󵄨ℎ𝑅𝑈𝐿 󵄨󵄨󵄨󵄨
.
=
󵄨2
󵄨 󵄨2 󵄨
𝛾 (󵄨󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 + 󵄨󵄨󵄨󵄨ℎ𝑅𝑈𝐿 󵄨󵄨󵄨󵄨 ) + 1
(43)
𝛾 (𝑚𝑋 , 𝑥 (𝑚𝑋 /Ω𝑋 ))
𝐹|̃ℎ𝑋 |2 (𝑥) =
Γ (𝑚𝑋 )
=1−𝑒
𝑘
𝑓|ℎ𝑋 |2 (𝑥) = 𝑄 ∑ (−1)
𝑘=0
𝑛
𝑚
1
.
∑ ( 𝑋 𝑥)
Ω
𝑛!
𝑋
𝑛=0
(𝑥) [𝐹|̃ℎ𝑋 |2 (𝑥)]
(44)
𝑙+𝑘−1
, (45)
𝐿−𝑙
𝑙+𝑘
(−1)𝑘 𝐿−𝑙
𝐶𝑘 [𝐹|̃ℎ𝑋 |2 (𝑥)] ,
𝑙+𝑘
𝑘=0
𝐹|ℎ𝑋 |2 (𝑥) = 𝑄 ∑
(48)
𝐽2
Then, by using (44) and (45), 𝐽2 can be calculated as
𝐿−𝑙 𝑚𝑆𝑅 −1
𝐽2 = 1 − 𝐽1 − 𝑄 ∑ ∑ (−1)𝑘 𝐶𝑘𝐿−𝑙
𝑘=0 𝑛=0
∞
1
𝑛!
𝑙+𝑘−1
⋅ ∫ 𝑓|̃ℎ𝑅𝑈 |2 (𝑥) (𝐹|̃ℎ𝑅𝑈 |2 (𝑥))
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
𝑙
𝑙
𝜂𝑙∗
(49)
𝜑
∗
× 𝑒−(𝜂𝑙 (1+𝛾𝑥)𝑚𝑆𝑅 /𝛾Ω𝑆𝑅 (𝑥−𝜂𝑙 )) (
𝑛
𝜂𝑙∗ (1 + 𝛾𝑥) 𝑚𝑆𝑅
) 𝑑𝑥.
𝛾Ω𝑆𝑅 (𝑥 − 𝜂𝑙∗ )
In (49), by using binomial expansion [72, eq. (1.111)], 𝜑
can be obtained in closed form as
𝑙+𝑘−1 𝑡(𝑚𝑅𝑈 −1)
∑ 𝐶𝑡𝑙+𝑘−1 (−1)𝑡
𝜑= ∑
𝑡=0
𝑝=0
⋅𝑒
𝑚𝑋 −1
𝐶𝑘𝐿−𝑙 𝑓|̃ℎ𝑋 |2
𝜂∗ (1 + 𝛾𝑥)
+ ∫ 𝑓|ℎ𝑅𝑈 |2 (𝑥) 𝐹|ℎ𝑆𝑅 |2 ( 𝑙
) 𝑑𝑥.
𝑙
𝛾 (𝑥 − 𝜂𝑙∗ )
𝜂𝑙∗
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
∞
(50)
−𝑥(𝑚𝑅𝑈 𝑡/Ω𝑅𝑈 ) 𝑝
In (44), right hand side of the equation is obtained
by using the series expansion form of incomplete Gamma
function [72, eq. (8.352.6)] and 𝑚𝑋 denotes the Nakagami-𝑚
parameter belonging to the link 𝑋.
Furthermore, the PDF and CDF of the ordered squared
envelope |ℎ𝑋 |2 can be written by using (44) as [89]
𝐿−𝑙
𝑃out,𝑙 = ∫ 𝑓|ℎ𝑅𝑈 |2 (𝑥)
𝑙
⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟
0
∗
Since channel parameters are Nakagami-𝑚 distributed,
|̃ℎ𝑋 |2 squared envelope of any unordered link 𝑋, where 𝑋 ∈
{𝑆𝑅, 𝑅𝑈𝑙 }, follows Gamma distribution with CDF
−𝑥(𝑚𝑋 /Ω𝑋 )
The OP expression given in (47) can be mathematically
rewritten as
𝐽1
In order to provide notational simplicity, we assume that 𝑃𝑠 =
𝑃𝑅 = 𝑃, 𝜎𝑅2 = 𝜎𝑈2 𝑙 = 𝜎2 . In addition, 𝛾 = 𝑃/𝜎2 denotes the
average SNR.
After the SIC process implemented at the receiver of 𝑈𝑙 ,
the SINR for the 𝑙th user can be obtained as [89]
𝛾𝑅𝑈𝐿
󵄨
󵄨2
𝜂𝑙∗ (1 + 𝛾 󵄨󵄨󵄨󵄨ℎ𝑅𝑈𝑙 󵄨󵄨󵄨󵄨 )
(47)
󵄨󵄨2
󵄨󵄨
2
󵄨
∗ 󵄨󵄨
).
− Pr (󵄨󵄨󵄨ℎ𝑅𝑈𝑙 󵄨󵄨󵄨 > 𝜂𝑙 , 󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 >
󵄨󵄨2
󵄨󵄨
𝛾 (󵄨󵄨󵄨ℎ𝑅𝑈𝑙 󵄨󵄨󵄨 − 𝜂𝑙∗ )
𝜂𝑙∗
𝑃
.
𝐺 = √ 󵄨 󵄨𝑅2
󵄨
𝑃𝑠 󵄨󵄨ℎ𝑆𝑅 󵄨󵄨󵄨 + 𝜎𝑅2
𝛾𝑅𝑈𝑙
4.1.1. Outage Probability of Cooperative NOMA. By using the
approach given in [89], the OP of the 𝑙th user can be written
as
(46)
where 𝑄 = 𝐿!/(𝐿 − 𝑙)!(𝑙 − 1)! and 𝐶𝑘𝐾 = ( 𝐾𝑘 ) represents the
binomial combination.
𝑥 𝜗𝑝 (𝑡, 𝑚𝑅𝑈) ,
where 𝜗𝑎 (𝑏, 𝑔𝑐 ) denotes multinomial coefficient given in (26).
Furthermore, if we substitute derivative of (44) and (50)
into (49) and then by using some algebraic manipulations, 𝐽2
can be obtained in closed form. Then, by substituting 𝐽2 into
(48), we can obtain the OP of 𝑙th user in closed form as
𝑃out,𝑙 = 1 − 𝑄 ∑
𝑘,𝑛,𝑡,𝑝,𝑖,𝑞
⋅
⋅
(−1)𝑡+𝑘 𝐶𝑘𝐿−𝑚 𝐶𝑡𝑙+𝑘−1 𝐶𝑖𝑛 𝐶𝑞𝑝+𝑚𝑅𝑈 −1
𝜗𝑝 (𝑡, 𝑚𝑅𝑈)
𝑛!Γ (𝑚𝑅𝑈)
×(
𝜌(𝑖+𝑞+1)/2
(𝑡 + 1)(𝑞−𝑖+1)/2
∗
𝑚𝑅𝑈 (2𝑚𝑅𝑈 −𝑞+𝑖−1)/2
)
Ω𝑅𝑈
(
𝑚𝑆𝑅 𝑛−𝑖 ∗𝑛−𝑖+𝑝+𝑚𝑅𝑈 −1−𝑞
) 𝜂𝑙
Ω𝑆𝑅
∗
× 𝑒−(𝜂𝑙 𝑚𝑅𝑈 (𝑡+1)/Ω𝑅𝑈 ) 𝑒−(𝜂𝑙 𝑚𝑆𝑅 /Ω𝑆𝑅 ) × 2
× 𝐾𝑞−𝑖+1 (2√
𝜌𝑚𝑅𝑈 (𝑡 + 1)
),
Ω𝑅𝑈
(51)
Wireless Communications and Mobile Computing
17
100
100
mSR = mRU = 1
mSR = mRU = 1
10
10
Outage probability
Outage probability
10−1
−2
10−3
mSR = mRU = 2
10−4
10−5
5
10−2
10−3
mSR = mRU = 2
10−4
10−5
Dashed and solid line:
Simulation
0
−1
10
15
SNR (dB)
20
25
30
10−6
Dashed and solid line:
Simulation
0.1
0.2
0.3
0.4
0.5
dSR
0.6
0.7
0.8
0.9
U1 Theo
U2 Theo
U3 Theo
U1 Theo
U2 Theo
U3 Theo
Figure 9: Outage probability of NOMA versus SNR in case 𝑑𝑆𝑅 =
0.5 and different Nakagami-𝑚 parameters.
Figure 10: Outage probability of NOMA versus 𝑑𝑆𝑅 in case 𝛾 =
20 dB and different Nakagami-𝑚 parameters.
5. Practical Implementation Aspects
where the binomial expansion [72, eq. (1.111)] and the integral
representation in [72, eq. (3.471.9)] are used for the derivation. In (51), 𝜌 = 𝜂𝑙∗ 𝑚𝑆𝑅 (1 + 𝛾𝜂𝑙∗ )/𝛾Ω𝑆𝑅 and ∑𝑘,𝑛,𝑡,𝑝,𝑖,𝑞 ≡
𝑚 −1
𝑡(𝑚
−1)
𝑝+𝑚
−1
𝑙+𝑘−1
𝑆𝑅
𝑅𝑈
∑𝐿−𝑙
∑𝑛𝑖=0 ∑𝑞=0 𝑅𝑈 (⋅) notations are
𝑘=0 ∑𝑛=0 ∑𝑡=0 ∑𝑝=0
used to provide a short hand representation. 𝐾V (⋅) denotes
the Vth order modified Bessel function of second kind [72, eq.
(8.407.1)]. The OP expression in (51) is in a simpler form when
compared to equivalent representations in the literature.
4.1.2. Numerical Results of Cooperative NOMA. In this section, we provide numerical examples of the provided theoretical results obtained for the OP of NOMA and validate them
by Monte Carlo simulations. We assume that the distances
between the BS and the mobile users are normalized to one,
−𝜅
and Ω𝑅𝑈 = (1 − 𝑑𝑆𝑅 )−𝜅 , where 𝜅 = 3 is the
so that Ω𝑆𝑅 = 𝑑𝑆𝑅
path loss exponent. In all figures, 𝐿 = 3 users and 𝑎1 = 1/2,
𝑎2 = 1/3, 𝑎3 = 1/6, 𝛾th1 = 0.9, 𝛾th2 = 1.5, 𝛾th3 = 2 parameters
have been used.
In Figure 9, we present the OP performance of NOMA
versus SNR. As can be seen from the figure, theoretical
results are well matched with simulations. In addition, OP
performances of the second and third users are better than
that of the first user and also the same at high SNR region.
Moreover, as the channel parameters increase, the OPs of all
users increase.
Figure 10 plots the OP performance of NOMA versus
the normalized distance between the BS and the relay. As
seen from the figure, while the optimal relay location of the
user with the strongest channel condition is near the BS,
the other users’ optimal relay locations are far from the BS
since the user with worse channel has higher power allocation
coefficient.
In the literature, power allocation and user clustering are
generally considered as the main problems in NOMA systems, and several strategies are proposed to provide efficient
solutions to these issues. As also considered in [131–133],
these problems are formulated as an optimization problem
and the corresponding solution procedures are also proposed. Besides these, studies, such as [54, 134, 135], propose approaches that are suitable to real-time applications.
Imperfect CSI is assumed in the corresponding system models. However, real-time implementation challenges are not
considered in most of the studies and the associated implementation design, which may provide effective solutions to
these challenges, is not mentioned. In this section, these
challenges are highlighted and important design components
are explained. In the following subsection, some studies that
include real-time implementation of NOMA are mentioned
and challenges of such real-time implementations will be
detailed.
5.1. Related Works. The number of studies that target realtime implementation of NOMA is very limited. To the
best of the authors’ knowledge, beyond three main studies,
such content is not included in any other study at the
time of preparation of this paper. In [136], single user(SU-) MIMO is integrated to downlink and uplink NOMA,
and extensive computer simulations provide detailed rate
evaluation between OMA and NOMA methods. Moreover,
a comprehensive testbed is created to experiment downlink
NOMA with SU-MIMO setup under real-time impairments.
Turbo encoding is also utilized in the implementation and a
SIC decoding structure, which also includes turbo decoding
and MIMO detection, is proposed. Due to usage of a wider
18
bandwidth, NOMA provides data rate improvement of 61%
in this experiment scenario. Reference [137] targets improper
power allocation issue, which is seen as a performance
limiting factor in conventional NOMA models. By exploiting
the physical-layer network coding (PNC) in NOMA, the
authors propose network-coded multiple access (NCMA).
Adaptation of PNC provides an additional transmission
dimension, and the received signals via two different dimensions increase the throughput significantly when compared
to the conventional NOMA systems. It is validated by experimental results that the proposed NCMA variations provide
noticeable performance improvements under the powerbalanced or near power-balanced scenarios. As the final
study, in [138], software defined radio (SDR) implementation
of downlink NOMA is realized to evaluate the performance
differences between NOMA and OMA techniques. Moreover,
protocol stack of LTE is modified to propose a suitable
protocol stack for NOMA. Besides these multilayer modifications, detailed experiments are also carried out. Measurement
results demonstrate the performance advantages of NOMA
over OMA.
Since superposition coding and NOMA are very similar
in context, studies on superposition coding also contain the
same valuable outcomes. In [139], advantages of superposition coding over time division multiplexing approach in
terms of improving the quality of the poor links are validated
via an SDR platform. Accordingly, the packet error rate is
measured and need of a joint code optimization is shown.
Moreover, an improved packet error rate performance that is
obtained with superposition coding, when compared to the
results of time division multiplexing utilization, is demonstrated. Similarly in [140], the authors propose a scheduler
based on superposition coding and it is demonstrated that
superposition coding based resource allocation can provide
a data rate improvement up to 25% when compared to the
orthogonal access techniques.
These studies provide significant insights about realtime implementation aspects of NOMA. However, several
practical challenges are not yet considered in available works.
5.2. Implementation Challenges. Practical implementation
challenges of NOMA are considered in some surveys. In
[141], the authors focus on multicell NOMA and the related
design issues in the environment in the presence of a strong
intercell interference (ICI). Since future wireless networks
are expected to be densely deployed, NOMA technique
is considered to be a candidate technique. ICI should be
considered due to the potential effects of interference between
adjacent BSs. Theoretical details of single-cell and multicell
NOMA solutions are detailed and the capacity analysis is
provided. Moreover, some major implementation issues are
highlighted. Hardware complexity and error propagation
issues of SIC implementation are detailed. Then, the importance of CSI is highlighted and the damaging effects of
imperfect CSI on the performance of NOMA are explained.
Multiuser power allocation and clustering are also emphasized. To limit ICI between adjacent cells, the authors propose
that users should be clustered properly and power allocation
mechanism should be operated efficiently. Integration of
Wireless Communications and Mobile Computing
fractional frequency reuse with NOMA is also considered
as a major challenge and such integration should be allocated properly to obtain significant gains. Lastly, security is
highlighted as another challenge, and the implementation
of physical layer security techniques is seen as a difficult
task. As demonstrated with computer simulations targeting
to demonstrate the performance limitation of interference,
proper ICI cancellation is very significant to obtain a robust
performance in multicell NOMA systems.
In [142], challenges of downlink and uplink NOMA
implementations and their implementation differences are
explained. As the first challenge, implementation complexity is highlighted, where it is pointed out that downlink
NOMA brings more complexity because of the utilization
of iterative detection procedures multiple times at multiple
receive nodes, when compared to the central receiver node,
as applicable in uplink NOMA systems. Secondly, intracell/intracluster interference is stated as a crucial issue for
both systems due to interference effects between users. As
the third challenge, SIC receivers which are implemented
differently in downlink and uplink cases are considered.
Lastly, ICI is elaborated. It is shown that ICI is more effective
in uplink case and could limit performance significantly.
However, it is not that effective in downlink case and the
observed performance degradation is comparable to that of
observed in OMA systems. Moreover, some critical points
are listed. Firstly, propagation errors in SIC receivers are
mentioned as an important performance limiting factor and
interference cancellation schemes are considered necessary
to improve these effects. Secondly, multicell NOMA is highlighted, where obtaining the same single-cell NOMA gains
over OMA in multicell scenarios becomes challenging. User
grouping/scheduling, power allocation, and ICI mitigation
are also considered as crucial items to obtain an improved
performance. Besides these implementation issues, integration of NOMA-based wireless backhauling to small cells and
cooperative schemes are highlighted as necessary precautions
to increase NOMA’s applicability in real-time.
In [143], implementation issues of NOMA are discussed
and listed. Decoding complexity, error propagation, and
errors that faced power balanced scenarios are also mentioned. As less considered issues, quantization errors that lead
to degradation of weak signals, power allocation complexity
due to difficulty of optimization of proper power levels to all
users, residual timing offset that leads to synchronization loss,
and error increment are highlighted. Furthermore, signaling
and processing overhead due to learning procedure of CSI are
also listed as a critical inefficiency source.
Some of the main problems that are mentioned in these
studies and other issues that are not yet discussed in the
literature will be listed and detailed below.
(1) Hardware Complexity. When compared to OMA, NOMA
causes increased complexity on the hardware side due to SIC
implementation. To obtain the users’ symbols that transmit
or receive with lower power symbols, high power symbols
are required to be estimated first with the SIC detector. If the
number of users especially is high or fast signal transmission
is required, the SIC procedure that is used multiple times,
Wireless Communications and Mobile Computing
in addition to the detection delay, could cause important
limitations for battery-limited devices. Since longer battery
life is desired in consumer electronics, implementation of
NOMA, particularly in dense networks, could be inefficient. This issue may limit usage of NOMA. Effective user
clustering and power allocation are crucial to alleviate this
problem.
(2) Error Propagation in SIC Implementation. According to
the main principle of NOMA, on the receiver side, the
user with better channel conditions is estimated first via
SIC detection. Therefore, the success of the reception of
main signal depends on successful estimation of the high
power signals. Since channel and hardware impairments
are effective in the reception process, SIC detection can
be negatively affected. It is not straightforward for NOMA
systems to ideally estimate channel, due to the presence of
carrier frequency offset (CFO), timing offset (TO), and other
hardware related impairments. Thus, erroneous detection
and error propagation are probable in the SIC detection
process. To overcome this and to improve the transmission
quality, more robust solutions are necessary. Rather than
changing the main detector components, improving the
estimation quality of mentioned impairments is a more
effective approach to obtain a practical performance gain.
(3) Optimal Pilot Allocation. Since multiple signals are
transmitted in an overlapped fashion, interference emerges
and error performance starts to degrade in NOMA, when
compared to OMA systems. It is a clear fact that perfect or
near-perfect CSI is a must to obtain a good performance. Pilot
positions and the number of allocated pilots are important
design considerations in NOMA implementation. These are
critical even in OMA systems due to uncertain channel
characteristics in wireless communication environments.
However, due to the inherent interference, optimal pilot
allocation is more critical for NOMA systems and careful
design is required. Therefore, channel characteristics should
be tracked efficiently and accurately to allocate sufficient
number of pilots at proper positions, which could result in
good error performance in NOMA systems.
(4) Instantaneous CSI Requirement. Besides pilot allocation
issues in NOMA implementations, another basic CSI estimation issue exists in this process. Allocation of a previously
allocated frequency band to a secondary user brings a serious
problem; CSI for the transmission of this user should be
estimated with orthogonal transmissions. This inevitably
blocks the transmission of main user and results in an
unfavorable situation. It is not clear whether this issue can be
tolerated or not in real-time. Moreover, in dense networks,
instantaneous band allocation may be required and, in these
cases, this issue may become more critical. Effective and
practical solution to this problem is very important for the
future of NOMA systems. As a road map suggestion, pilot
contamination problem in massive MIMO systems may be
considered and corresponding solutions like [144] may be
applied to NOMA systems. However, differences between the
logics of these techniques should also be taken into account.
19
(5) Carrier Frequency Offset and Timing Offset Estimation.
Due to the nature of wireless devices, CFO and TO emerge
frequently during communication. Low-quality clocks especially that are included in such devices cause significant CFO
and TO, thus, leading to a significantly degraded transmission quality. Usage of multicarrier waveforms like OFDM
renders robust CFO and TO estimation and provides the necessary correction. In the point-to-point OMA transmissions,
joint estimation of CFO and TO is quite straightforward
due to distinguishability of received signals. Even in these
cases, these impairments could cause serious performance
degradation. However, this is not valid for NOMA because
of the reception of signals in an overlapped fashion. This
issue has not yet been considered in the literature. Effective
solutions and practical approaches are required to guarantee
a good transmission quality in NOMA. Highly accurate
synchronization support to devices can overcome such disturbances; however, lower cost expectations prevent such
a solution. Therefore, particularly, in uplink transmissions,
distinguishability of overlapped signals should be achieved.
5.3. Lessons Learned. In order to capture the full set of
advantages of NOMA in real-time that are validated in
the theoretical studies, possible major challenges should be
investigated and a comprehensive implementation strategy
that overcomes these challenges should be determined. There
are few studies in the literature that list these challenges, but
there are some challenges that have not yet been considered.
From this perspective, in this section, previously mentioned
challenges are evaluated and important ones are given with
other undetected major challenges. These also provide topics that deserve attention from the researchers who target
improving NOMA’s applicability.
6. Conclusion
NOMA schemes are proposed to improve the efficient usage
of limited network sources. OMA based approaches that use
time, frequency, or code domain in an orthogonal manner
cannot effectively utilize radio resources, limiting the number
of users that can be served simultaneously. In order to
overcome such drawbacks and to increase the multiple access
efficiency, NOMA technique has been recently proposed.
Accordingly, users are separated in the power domain. Such a
power-domain based multiple access scheme provides effective throughput improvements, depending on the channel
conditions.
In OMA, differences between channels and conditions
of users cannot be effectively exploited. It is quite possible
for a user to be assigned with a large frequency band
while experiencing deteriorating channel conditions. Such
user cases limit the effectiveness of OMA based approaches.
However, according to the NOMA principle, other users
who may be experiencing better channel conditions can
use these bands and increase their throughput. Moreover,
corresponding users who are the primary users of these bands
continue to use these bands. In such deployments, power level
of users is selected in a way to target a certain maximum
error rate. Furthermore, the performance of NOMA can
20
be significantly improved using MIMO and cooperative
communication techniques.
In this paper, we provide a unified model system model
for NOMA, including MIMO and cooperative communication scenarios. Implementation aspects and related open
issues are detailed. A comprehensive literature survey is also
given to provide an overview of the state-of-the-art.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
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